Accelerating relaxation dynamics in open quantum systems with Liouvillian skin effect

We investigate a non-Hermitian model featuring nonreciprocal gradient hoppings. Through an in-depth analysis of the Liouvillian spectrum and dynamics, we confirm the emergence of the Liouvillian skin effect resulting from the nonreciprocal nature of hoppings in this model. Furthermore, we observe that the presence of gradient hopping strength leads to an accelerated relaxation time for the system. Through numerical investigations of the Liouvillian gap, relaxation time, and steady-state localization length, we discover that the relaxation time in this model cannot be explained by the currently established relationship associated with the Liouvillian skin effect. This discrepancy highlights the need for further exploration and theoretical advancements to fully comprehend the intricate mechanisms underlying quantum relaxation processes. Motivated by these findings, we propose a theoretical approach to realize this non-Hermitian model in an atomic system with a sideband structure by employing an adiabatic elimination technique. These results contribute to our deeper comprehension of quantum relaxation dynamics and provide theoretical backing for the development of techniques aimed at controlling quantum relaxation processes.